A397200 - OEIS

%I #4 Jun 18 2026 00:46:15

%S 1,1,1,9,8,7,8,1,0,7,7,3,6,2,3,0,3,0,3,6,8,1,3,3,3,2,7,1,7,3,8,6,1,5,

%T 2,1,2,1,9,7,9,7,8,1,0,5,3,0,6,1,4,3,3,9,3,5,5,3,0,0,0,4,8,5,8,0,2,3,

%U 2,9,1,1,1,1,1,8,6,2,6,4,9,3,8,8,9,1,7,1,8,3,5,0,0,2,4,4,6,6,8,8,4,6,1,3,0,7

%N Decimal expansion of Sum_{k>=1} AH(k)/k^3, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic (or skew-harmonic) number.

%H Cornel Ioan Vălean, <a href="https://doi.org/10.1007/978-3-031-21262-8">More (Almost) Impossible Integrals, Sums, and Series</a>, Springer Cham, 2023. See section 4.22, p. 425.

%H <a href="/index/Ha#harmonic">Index entries for sequences related to harmonic numbers</a>.

%F Equals 7*log(2)*zeta(3)/4 - 5*zeta(4)/16.

%e 1.119878107736230303681333271738615212197978105306143...

%t RealDigits[7*Log[2]*Zeta[3]/4 - 5*Zeta[4]/16, 10, 120][[1]]

%o (PARI) 7*log(2)*zeta(3)/4 - 5*zeta(4)/16

%Y Cf. A058312, A058313.

%Y Cf. A002117, A002162, A013661, A013662.

%Y Sum_{k>=1} AH(k)/k^m: A397199 (m=2), this constant (m=3), A397201 (m=4).

%K nonn,cons

%O 1,4

%A _Amiram Eldar_, Jun 18 2026